Details

sample504.0ms

Algorithm

intervals

Results

194.0ms	52×	body	2560	valid
142.0ms	77×	body	1280	valid
51.0ms	59×	body	640	valid
16.0ms	30×	body	320	valid
9.0ms	22×	body	160	valid
4.0ms	16×	body	80	valid

simplify27.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	19
3	19
2	17
1	13
0	6

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.2b

localize59.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.2b	(- x (tan x))
1.2b	(- x (sin x))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

43×	`add-sqr-sqrt` `*-un-lft-identity`
25×	`times-frac`
15×	`add-cube-cbrt`
14×	`distribute-lft-out--` `difference-of-squares`
7×	`add-log-exp`
5×	`associate-/r` `add-cbrt-cube` `add-exp-log` `associate-/l`
4×	`flip3--` `flip--`
3×	`pow1` `insert-posit16`
2×	`sub-neg` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-sub` `div-exp` `div-inv`

Counts

3 → 83

Calls

3 calls:

34.0ms	(/ (- x (sin x)) (- x (tan x)))
4.0ms	(- x (tan x))
7.0ms	(- x (sin x))

series218.0ms

Counts

3 → 9

Calls

3 calls:

99.0ms	(/ (- x (sin x)) (- x (tan x)))
58.0ms	(- x (tan x))
60.0ms	(- x (sin x))

simplify960.0ms

Counts

92 → 92

Iterations

Iter	Nodes
done	2010
3	2010
2	964
1	375
0	160

prune872.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* x x) 9/40)
0.1b	(* (* x x) (* x x))
0.4b	(* (* (* x x) (* x x)) 27/2800)
15.1b	(- (- (* (* x x) 9/40) 1/2) (* (* (* x x) (* x x)) 27/2800))

rewrite334.0ms

Algorithm

rewrite-expression-head

Rules

138×	`pow1`
39×	`add-cbrt-cube` `pow-prod-down` `add-exp-log`
36×	`pow-prod-up`
24×	`prod-exp` `cbrt-unprod`
22×	`pow-sqr`
18×	`pow-plus`
13×	`pow2`
9×	`add-log-exp`
8×	`add-sqr-sqrt`
7×	`associate-r`
6×	`*-un-lft-identity` `add-cube-cbrt`
4×	`insert-posit16`
3×	`diff-log` `associate-l` `*-commutative` `unswap-sqr`
2×	`sub-neg` `associate--l+`
1×	`associate--l-` `flip3--` `swap-sqr` `flip--`

Counts

4 → 130

Calls

4 calls:

24.0ms	(* (* x x) 9/40)
27.0ms	(* (* x x) (* x x))
96.0ms	(* (* (* x x) (* x x)) 27/2800)
184.0ms	(- (- (* (* x x) 9/40) 1/2) (* (* (* x x) (* x x)) 27/2800))

series210.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(* (* x x) 9/40)
39.0ms	(* (* x x) (* x x))
60.0ms	(* (* (* x x) (* x x)) 27/2800)
72.0ms	(- (- (* (* x x) 9/40) 1/2) (* (* (* x x) (* x x)) 27/2800))

simplify1.1s

Counts

142 → 142

Iterations

Iter	Nodes
done	2007
3	2007
2	1193
1	403
0	135

prune964.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* x x) 9/40)
0.1b	(* (* x x) (* x x))
0.4b	(* (* (* x x) (* x x)) -27/2800)
15.1b	(+ (* (* x x) 9/40) (+ (* (* (* x x) (* x x)) -27/2800) -1/2))

rewrite404.0ms

Algorithm

rewrite-expression-head

Rules

138×	`pow1`
39×	`add-cbrt-cube` `pow-prod-down` `add-exp-log`
36×	`pow-prod-up`
24×	`prod-exp` `cbrt-unprod`
22×	`pow-sqr`
18×	`pow-plus`
13×	`pow2`
9×	`add-log-exp`
8×	`add-sqr-sqrt`
7×	`associate-r`
6×	`*-un-lft-identity` `add-cube-cbrt`
4×	`insert-posit16`
3×	`sum-log` `associate-l` `*-commutative` `unswap-sqr`
1×	`+-commutative` `associate-+r+` `flip3-+` `swap-sqr` `flip-+`

Counts

4 → 127

Calls

4 calls:

26.0ms	(* (* x x) 9/40)
22.0ms	(* (* x x) (* x x))
97.0ms	(* (* (* x x) (* x x)) -27/2800)
255.0ms	(+ (* (* x x) 9/40) (+ (* (* (* x x) (* x x)) -27/2800) -1/2))

series211.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(* (* x x) 9/40)
53.0ms	(* (* x x) (* x x))
49.0ms	(* (* (* x x) (* x x)) -27/2800)
61.0ms	(+ (* (* x x) 9/40) (+ (* (* (* x x) (* x x)) -27/2800) -1/2))

simplify1.6s

Counts

139 → 139

Iterations

Iter	Nodes
done	2005
3	2005
2	1268
1	421
0	135

prune1.0s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin x) (- x (tan x)))
1.0b	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
1.2b	(- x (tan x))
1.2b	(- x (tan x))

rewrite128.0ms

Algorithm

rewrite-expression-head

Rules

54×	`*-un-lft-identity`
44×	`add-sqr-sqrt`
33×	`times-frac`
18×	`distribute-lft-out--`
16×	`add-cube-cbrt`
12×	`difference-of-squares`
10×	`add-log-exp`
6×	`flip3--` `add-cbrt-cube` `add-exp-log` `associate-/r/` `flip--`
5×	`associate-/r*`
4×	`pow1` `insert-posit16`
3×	`sub-neg` `distribute-rgt-out--` `diff-log` `div-inv` `associate-/l*`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `frac-sub` `sub-div`

Counts

4 → 98

Calls

4 calls:

15.0ms	(/ (sin x) (- x (tan x)))
93.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
9.0ms	(- x (tan x))
9.0ms	(- x (tan x))

series503.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(/ (sin x) (- x (tan x)))
260.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
64.0ms	(- x (tan x))
69.0ms	(- x (tan x))

simplify1.0s

Counts

110 → 110

Iterations

Iter	Nodes
done	2000
3	2000
2	1111
1	392
0	180

prune902.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes97.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.4b

bsearch202.0ms

Steps

Iters	Range		Point
8	0.0042870261776910435	186.95626557948964	0.028563011272804206
9	-0.35383103211093586	-9.60334830165094e-09	-0.029021700279035747

simplify8.0ms

Iterations

Iter	Nodes
done	28
1	28
0	24

end0.0ms

sample15.6s

Algorithm

intervals

Results

7.2s	1626×	body	2560	valid
5.0s	2728×	body	1280	valid
2.1s	1903×	body	640	valid
772.0ms	928×	body	320	valid
233.0ms	440×	body	160	valid
85.0ms	375×	body	80	valid